1. The angle of deformation of an automobile unibody as a result of a head-on collision (in test conditions) is modeled with a Weibull distribution F (x) = 1 e_["/5), x > 0, having shape parameter [3 = 1.1728 and scale parameter 5 = 1.2750. A plot of the density function is shown below. 0.8- 0.5- ' f 0.1- HEIDUII 0.3- den-lty 0.2' 0.1- 0.0- a) Find the probability that three independent head-on collisions will each have an angle of deformation greater than 1.5. b) Determine the 20 th percentile of deformation angle. c) The mean of this distribution is pi = 1.1643 and the standard deviation is 0' = 0.9960. Suppose a random sample 78 independent test crashes will be observed. What is the (approximate) chance that the sample mean will exceed 1.30